Here is an example of a cast sheet, which showed who performed in the episode. This one is for "Koko Kate", Season 3, Episode 38. Unfortunately, it does not mention the musicians or minor background characters. The second sheet has the home addresses of the stars, their pay schedule and who their agents were:

I was re-reading the BigBro's "Sound of Tiki" liner notes on the show. Apparently the cast was never in Hawaii, it was all done on the Warner Brothers soundstage in Burbank !! Even the Hawaiian Village Shell Bar was a set. I guess they had a Hawaiian crew who did the local shooting which was used as rear projection for the actors.